Solve the following inequation and represent the solution set on the number line $2 x - 5 \leq 5 x + 4 < 11$ where $x \in I$ .

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Solution

Step 1- Solve the inequation:
$2 x - 5 \leq 5 x + 4 < 11$
$2 x - 5 \leq 5 x + 4$ and $5 x + 4 < 11$
$- 9 \leq 3 x$ and $5 x < 7$
$x \geq - 3$ and $x < \frac{7}{5}$
Step 2-Representation on the number line:
The solution set will be $- 3 \leq x < \frac{7}{5}$ , so the solution set on the number line will be $x = {- 3, - 2, - 1, 0, 1}$
Hence the solution set of the inequality $2 x - 5 \leq 5 x + 4 < 11$ where $x \in I$ is $x = {- 3, - 2, - 1, 0, 1}$ and the solution set on the number line is as shown above.

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